Question

find the value of the determinant $\left[\begin{array}{ccc}a^{2} +b^{2} &a^{2} -c^{2} &a^{2} -c^{2}\\-a^{2} &0&c^{2} -a^{2} \\b^{2} &-c^{2} &b^{2} \end{array}\right]$

please give the complete solution the answer is 0 _/\_

Answer 1

ɢɪᴠᴇɴ→

$\left[\begin{array}{ccc}a^{2} +b^{2} &a^{2} -c^{2} &a^{2} -c^{2}\\-a^{2} &0&c^{2} -a^{2} \\b^{2} &-c^{2} &b^{2} \end{array}\right]$

ᴛᴏ ꜰɪɴᴅ→

Value of determinant

ꜱᴏʟᴜᴛɪᴏɴ→

Refer attached image for your answer.

Hope it's helpful.^_^

Answer 2

The first thing you do in this problem is to factor out the x.

x³ - 5x² + 6x = 0

x(x²-5x+6) = 0

x(x-3)(x-2)=0

x=0, (x-3)=0, (x-2)=0

x={0, 2, 3}